This section is intended to introduce the reader to various aspects of art, which may be associated with embodiments of the present invention. This discussion is believed to be helpful in providing the reader with information to facilitate a better understanding of particular techniques of the present invention. Accordingly, it should be understood that these statements are to be read in this light, and not necessarily as admissions of prior art.
Drill tool assembly vibration is one of the primary Rate of Penetration (ROP) limiters encountered during drilling operations. Drill tool assemblies vibrate during drilling for a variety of reasons, each of which may be said to be related to a drilling parameter. For example, the rotary speed, weight on bit, mud viscosity, etc. each may affect the vibrational tendency of a given drill tool assembly during a drilling operation. Additionally or alternatively, the configuration of the drill tool assembly may influence the vibrational tendency of a drilling operation. Other factors beyond the control of the operators, such as the condition of the formation, may also influence the vibrational tendency of a drill tool assembly. As used herein, drilling parameters includes characteristics and/or features of both the drilling hardware (e.g., drill tool assembly) and the drilling operations.
The particular design of the drill tool assembly, in terms of the choice of drill tool assembly components and their relative placement with respect to each other, is known to have significant impact on the vibrations encountered during drilling. As used herein, drill tool assembly refers to assemblies of components used in drilling operations. Exemplary components that may collectively or individually be considered a drill tool assembly include rock cutting devices, bits, bottom hole assemblies, drill collars, drill pipes, drill strings, couplings, stabilizers, etc. Conventional efforts to determine the vibration-related performance of a particular drill tool assembly configuration under the specific, realistic conditions of a drilling operation required deploying the design or resorting to sophisticated and computationally intensive models that require a large amount of time, computing power, and detailed input information that is usually not available. Deployment of vibrationally poor designs can result in loss of ROP, shortened drill tool assembly life, increased number of required trips, increased failure rate of downhole tools, and increased non-productive time. The cost of failures can vary from a few hundred thousand dollars to several millions of dollars depending on whether a round-trip of drill tool assembly is required or if there is a need to fish components stuck in the hole. Thus, it is desirable to provide the drilling engineer with a tool utilizing readily available data that can quickly analyze the vibrational tendencies of one or more considered drill tool assembly designs.
As described above, drilling parameters that may affect drilling vibrations include drilling operating conditions. Ranges and constraints on drilling operating conditions vary from one bit run to the next, so there is a need to study the effects of these changes on vibrational performance in an easy to use model. Several vibrational modes can affect the drilling performance; efforts to study each of these modes has to be posed and analyzed in a tractable manner. One approach to mitigate lateral drilling vibrations was presented in pending International Patent Publication No. WO2008/097303, which is incorporated herein by reference in its entirety for all purposes. That application presented methods for analyzing or evaluating alternative bottom hole assembly designs to determine the response of the alternative BHA systems under identical loading conditions. More specifically, WO2008/097303 discloses tools to evaluate the lateral vibration (whirl) tendency of BHA designs through the use of at least one vibration index. The models utilized by the tools are based on the forced harmonic response of the BHA to excitations at the bit, driven by the rotation rate (RPM) of the BHA and its harmonics. While these tools and associated models are effective at modeling and studying whirl vibrations, they only analyze lateral vibrations in the BHA. Other modes of vibration, such as axial and torsional vibrations, are influenced by the drill string in addition to the BHA. Due to the greater complexity of the entire drill tool assembly (e.g., the drill string and the BHA) and the nature of the interactions between the drill tool assembly and the wellbore, there is a need to develop tools, suitable models, and vibration indices for axial and torsional vibrations encountered by a drill tool assembly during operation.
Typically, severe axial vibration dysfunction can be manifested as “bit bounce,” which results in a lessening or even a complete loss of contact between the rock formation and the drill bit cutting surface through part of the vibration cycle. Dysfunctional axial vibration can occur at other locations in the drill tool assembly. Other cutting elements in the drill tool assembly could also experience a similar effect. Small oscillations in weight on bit (WOB) can result in drilling inefficiencies, leading to decreased ROP. Thus, there is a need to minimize the response of the drill tool assembly to axial excitations.
The primary torsional dysfunction is called “stick-slip”, which is primarily associated with instability in the rotation rate of the drill bit around its nominal value. Other types of torsional dysfunctions exist, including large forced oscillations that could cause fluctuations in the RPM.
Multiple efforts have been made to study and/or model these more complex torsional and axial vibrations, some of which are discussed here to help illustrate the advances made by the technologies of the present disclosure. For example, “Drill String Vibrations due to Intermittent Contact of Bit Teeth,” P. R. Paslay, 1962, Transactions of the ASME Paper No. 62-Pet-13 presents early work in the area of axial and torsional vibrations. This paper presents an analytical solution to the axial vibration problem. The model considers the entire drill tool assembly (from the bit to the kelly). The boundary condition at the kelly is treated as a fixed condition. The drill tool assembly is broken up into two sections: drill collars and drill pipe. An axial displacement excitation is specified at the bit. Forced frequency response is utilized to determine the steady state harmonic axial force that is generated at the bit due to the specified displacement excitation. The natural frequencies of the system are calculated analytically.
Other early work included “Longitudinal and Angular Drill-String Vibrations with Damping,” D. W. Dareing, Petroleum Mechanical Engineering and First Pressure Vessel and Piping Conference, Dallas, Tex., Sep. 22-25, 1968. The authors presented a mathematical model for studying axial and torsional vibration of drill tool assemblies. The entire drill tool assembly is modeled using wave equations based upon bar theory. A spring and mass are used to model the surface equipment. The equations are solved analytically, and the model allows for changes in pipe diameters.
DEA Project 29 was a multi-partner program initiated to develop modeling tools for analyzing drill tool assembly vibrations. In the research work, a transfer matrix was used to solve for the surface conditions, for a given initial displacement or initial force at the bit. The model of the drill tool assembly was composed of tubular elements. The program focused on the development of an impedance-based, frequency-dependent, mass-spring-dashpot model using a transfer function methodology for modeling axial and torsional vibrations. These transfer functions describe the ratio of the surface state to the input condition at the bit. The boundary conditions for axial vibrations consisted of a spring, a damper at the top of the drill tool assembly (to represent the rig) and a “simple” axial excitation at the bit (either a force or displacement). For torsional vibrations, the bit was modeled as a free end (no stiffness between the bit and the rock) with damping. The authors also commented on the effect of damping and included it in the model in the form of a constant selected to approximate the damping effect. The DEA Project 29 reports disclosed that the coupling between mud pressure fluctuation and drill pipe vibration should not be ignored. This work also indicated that downhole phenomena such as bit bounce and stick-slip are observable from the surface. While the DEA Project 29 recognized that various factors affect vibrational performance, the results of the research (i.e., models developed through the research) represented these factors simply by including one or more constants into the model. For example, the mud damping effect was represented in the models by a constant approximating the effect on vibration. Results of this effort were published as “Coupled Axial, Bending and Torsional Vibration of Rotating Drill Strings”, DEA Project 29, Phase III Report, J. K. Vandiver, Massachusetts Institute of Technology and “The Effect of Surface and Downhole Boundary Conditions on the Vibration of Drill strings,” F. Clayer et al, SPE 20447, 1990.
While the frequency-domain approaches that have been developed tend to be computationally tractable, the tractability derives from the almost singular focus on the primary factors affecting vibration, such as the weight on bit and the length of the drill string, and the use of approximating constants to represent the multitude of other factors that affect the severity and mode of vibration. While such approximations may be suitable in simple wells or in perfect wells, the application of such approximations and models to real-world wells is limited. For example, while the total impact of borehole damping effects and mud damping effects on vibrations may be small relative to the weight on bit, poor approximations of their affects can lead to significant changes in drilling efficiencies.
Moreover, the impact of these damping effects is difficult to approximate in transitioning from a model to an actual well, rendering the use of an approximation constant suitable in only the most limited of actual drilling operations. Consider, for example, a drilling operation that includes deviations in the well trajectory, such as to provide doglegs or directional drilling. In simple vertical wells, the drill tool assembly has contact points at the bit and at the rig (i.e., effectively no borehole damping effects). In more complex trajectories, or in more realistic representations of an actual wellbore, the drill tool assembly may contact the borehole at numerous locations along its length; the contact locations and characteristics may vary over time. These additional and varied contacts result in a distribution of additional forces exerted on the drill tool assembly along the well and over time. A model that fails to incorporate the effects of borehole damping will result in inaccurate vibration predictions leading to poor drill tool assembly design and/or inefficient drilling operations.
With the advent of more powerful computer systems, various attempts have been made to develop large scale, time-domain models of entire drill tool assemblies in complex wellbore trajectories, using finite element methods to resolve complex interactions between the various drill tool assembly elements, the drill bit, and the rock formation that is being drilled. Such methods have been disclosed in SPE 52821 and other publications, including U.S. Pat. Nos. 6,785,641 and 7,139,689. While powerful, such methods require a level of detail about the condition and trajectory of the borehole, rock properties, and bottom hole pattern, that are still very difficult and costly to obtain, if at all possible. They are also too computationally intensive to allow a rapid screening of various drilling scenarios for multiple drill tool assembly designs. Furthermore, the outputs of these models are complex and difficult to interpret.
Additionally, “The Genesis of Bit-Induced Torsional Drillstring Vibrations,” J. F. Brett, SPE 21943, 1992 describes a time-domain torsional vibration model that is described using two coupled differential equations. One equation described the stiff BHA attached to the drill pipe and the second equation described the upper end of the drill tool assembly, or surface drive system. The model was then solved using a Runge-Kutta simulation algorithm. Experimental friction curves relating the torque on bit as a function of the bit RPM were obtained for a sharp and a dull PDC bit. The experimental observations suggested that the torque on bit (i.e., stick-slip tendency) was proportional to the weight on bit for all observed bit speeds. These models and methods were implemented in the time-domain, requiring the computational intensity associated therewith.
While technologies related to torsional and axial vibration modeling have evolved, these technologies are still significantly limited by virtue of the assumptions and conditions used. As seen in the above discussion, the frequency-domain models previously developed have failed to account for complex relationships between the multiple segments of the drill tool assembly and the wellbore wall. Moreover, the finite-element based time-domain methods suffer from high computational complexity and cost, making them unsuitable for use as a routine analysis tool to evaluate large numbers of drilling scenarios in an efficient manner. Furthermore, the damping models used in these time- and frequency-domain methods are inadequate, omitting or oversimplifying the mud-drill tool assembly interactions. Accordingly, the need exists for systems and methods for mitigating drill tool assembly vibrations that utilizes the tractability and computational efficiency of frequency-domain models, but also allows consideration of more realistic drilling conditions such as complex wellbore trajectories (with or without doglegs), mud damping effects, velocity dependence of frictional forces, and complex boundary conditions at the surface and bit end. Additionally or alternatively, the need exists for systems and methods of evaluating two or more drill tool assembly configuration designs, for a given set of operating conditions, to determine which configuration design will experience the least torsional and/or axial vibrational dysfunction. Additionally or alternatively, the need exists for systems and methods to evaluate a given drill tool assembly configuration design to determine or predict operating conditions likely to result in lateral, axial, and/or torsional vibration, or alternatively, to result in minimizing lateral, axial, and/or torsional vibration.
Other related material may be found in at least U.S. Pat. No. 5,313,829; and in U.S. Patent Publication No. US 2007/0289778. Further, additional information may also be found in “Drillstring Torsional Vibrations: Comparison between Theory and Experiment on a Full-Scale Research Drilling Rig,” G. W. Halsey et al, SPE 15564, 1986; “A Study of Slip/Stick Motion at the Bit,” A. Kyllingstad and G. W. Halsey, SPEDE, December 1988, pp. 369-373; “Drillstring Stick-Slip Oscillations,” R. Dawson et al, 1987 SEM Spring Conference, Houston, Jun. 14-19, 1987; “Detection and Monitoring of the Slip-Stick Motion: Field Experiments,” M-P. Dufeyte and H. Henneuse, SPE/IADC 21945, 1991; “A Study of Excitation Mechanisms and Resonances Inducing Bottomhole-Assembly Vibrations”, A. Besaisow and M. Payne, SPE 15560, 1988; “Cost Savings through an Integrated Approach to Drillstring Vibration Control”, P. C. Kriesels, and W. J. G. Keultjes, SPE/IADC 57555, 1999; “Suppressing Stick-slip-induced Drillstring Oscillations: A Hyperstability Approach,” Van den Steen, L., 1997, PhD Thesis, University of Twente, The Netherlands; “H-∞ Control as Applied to Torsional Drillstring Dynamics,” Serrarens, A. F. A., 1997, MSc Thesis, Eindhoven University of Technology, The Netherlands; “On the Effective Control of Torsional Vibrations in Drilling Systems,” Tucker, R. W., and Wang, C., 1999, Journal of Sound and Vibration; Application of Neural Networks for Predictive Control in Drilling Dynamics”, D. Dashevshiy et al., SPE 56442, 1999; “Development of a Surface Drillstring Vibration Measurement System”, A. A. Besaisow, et al., SPE 14327, 1985; “Torsional Resonance of Drill Collars with PDC Bits in Hard Rock,” Warren, SPE 49204, 1998; “Stick-slip Whirl Interaction in Drillstring Dynamics,” R. I. Leine, et al, Journal of Vibration and Acoustics, April 2002, Vol. 124, pp. 209-220; “Analysis of the Stick-slip Phenomenon Using Downhole Drillstring Rotation Data,” Robnett, E. W., Hood, J. A., Heisig, G., and Macpherson, J. D., SPE/IADC 52821; “The Effects of Quasi-Random Drill Bit Vibrations Upon Drillstring Dynamic Behavior,” Skaugen, E., 1987, SPE 16660; “An Analytical Study of Drill String Vibrations,” Li, C., 1987, SPE 15975; “Mathematical Analysis of the Effect of a Shock Sub on the Longitudinal Vibrations of an Oilwell Drill String,” Kreisle, L. F., and Vance, J. M., 1970, SPE 2778; “Downhole Vibration Monitoring & Control System Quarterly Technical Report #2,” M. E. Cobern, et al, 2003, DOE Award Number: DE-FC26-02NT41664, APS Technology Inc.; and “Application of High Sampling Rate Downhole Measurements for Analysis and Cure of Stick-Slip in Drilling,” D. R. Pavone and J. P. Desplans, 1994, SPE 28324.